Question

1. complete the tables for $f(x) = x$ and $g(x) = x^3$ and $h(x) = x^5$.

a. complete:

$x$	$f(x) = x$
$0$
$1$

b. complete:

$x$	$g(x) = x^3$
$0$
$1$

c. complete:

$x$	$h(x) = x^5$
$0$
$1$

remote learning week 2 - day 2
© 2021

Explanation:

Part a: For \( f(x) = x \)

Step1: When \( x = -1 \)

Substitute \( x = -1 \) into \( f(x) = x \), so \( f(-1) = -1 \).

Step2: When \( x = 0 \)

Substitute \( x = 0 \) into \( f(x) = x \), so \( f(0) = 0 \).

Step3: When \( x = 1 \)

Substitute \( x = 1 \) into \( f(x) = x \), so \( f(1) = 1 \).

The completed table for \( f(x)=x \) is:

\( x \)	\( f(x) = x \)
\( 0 \)	\( 0 \)
\( 1 \)	\( 1 \)

Part b: For \( g(x) = x^3 \)

Step1: When \( x = -1 \)

Substitute \( x = -1 \) into \( g(x) = x^3 \), we get \( g(-1)=(-1)^3=-1 \).

Step2: When \( x = 0 \)

Substitute \( x = 0 \) into \( g(x) = x^3 \), we get \( g(0)=0^3 = 0 \).

Step3: When \( x = 1 \)

Substitute \( x = 1 \) into \( g(x) = x^3 \), we get \( g(1)=1^3 = 1 \).

The completed table for \( g(x)=x^3 \) is:

\( x \)	\( g(x) = x^3 \)
\( 0 \)	\( 0 \)
\( 1 \)	\( 1 \)

Part c: For \( h(x) = x^5 \)

Step1: When \( x = -1 \)

Substitute \( x = -1 \) into \( h(x) = x^5 \), we get \( h(-1)=(-1)^5=-1 \).

Step2: When \( x = 0 \)

Substitute \( x = 0 \) into \( h(x) = x^5 \), we get \( h(0)=0^5 = 0 \).

Step3: When \( x = 1 \)

Substitute \( x = 1 \) into \( h(x) = x^5 \), we get \( h(1)=1^5 = 1 \).

The completed table for \( h(x)=x^5 \) is:

\( x \)	\( h(x) = x^5 \)
\( 0 \)	\( 0 \)
\( 1 \)	\( 1 \)

Answer:

Step1: When \( x = -1 \)

Substitute \( x = -1 \) into \( h(x) = x^5 \), we get \( h(-1)=(-1)^5=-1 \).

Step2: When \( x = 0 \)

Substitute \( x = 0 \) into \( h(x) = x^5 \), we get \( h(0)=0^5 = 0 \).

Step3: When \( x = 1 \)

Substitute \( x = 1 \) into \( h(x) = x^5 \), we get \( h(1)=1^5 = 1 \).

The completed table for \( h(x)=x^5 \) is:

\( x \)	\( h(x) = x^5 \)
\( 0 \)	\( 0 \)
\( 1 \)	\( 1 \)